Simultaneous selection for homogeneous multinomial populations based on entropy function: An empirical Bayes approach

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/27802

Title:	Simultaneous selection for homogeneous multinomial populations based on entropy function: An empirical Bayes approach
Authors:	Gupta,SS;Leu,LY;Liang,TC
Contributors:	統計研究所
Date:	1996
Issue Date:	2010-06-29 19:33:56 (UTC+8)
Publisher:	中央大學
Abstract:	Consider k independent m-cell multinomial populations pi(1),...,pi(k), where pi(i) has the associated cell probability vector (p) under tilde(i) = (p(il),...,p(im)), i = 1,...,k. The entropy theta(i) = theta((p) under tilde p(i)) = -Sigma(j=1)(m)p(ij) log p(ij) is used as a measure of homogeneity of the population pi(i). A Bayes selection rule relative to the Dirichlet prior distribution D-m(alpha(1),...,alpha(m)) is obtained for selecting all homogeneous populations compared with a standard theta(0). When the values of the parameters alpha(1),...,alpha(m) are unknown, an empirical Bayes selection rule is proposed and its corresponding asymptotic optimality is investigated. It is shown that the proposed empirical Bayes selection rule is asymptotically optimal relative to the class of Dirichlet prior distributions, and the associated regret risk converges to zero with a convergence rate of order O(exp(-tau k + ln k)) for some positive constant tau = tau(alpha(1),...,alpha(m)).
Relation:	JOURNAL OF STATISTICAL PLANNING AND INFERENCE
Appears in Collections:	[Graduate Institute of Statistics] journal & Dissertation

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